Linear Equations Flashcards
Free linear equations flashcards covering one- and two-step equations, variables on both sides, slope-intercept form, systems and linear inequalities. Flip each card, say the answer first, then mark what you know and drill what you miss.
Type the problems from this lesson and check each step.
How to study with these linear equations flashcards
- Read the front of the card and say or write your answer before you flip it.
- Flip the card, then mark I know this only if you were right without hesitating.
- Mark Review again for anything you missed, then use Review missed only to drill those cards.
- Pick one topic at a time, then shuffle all topics for a mixed review.
Study tips for linear equations
Do short rounds of 10 to 15 cards. Say the answer out loud before you flip, then use Review missed only until the pile is empty. Come back the next day: spacing your practice beats one long session.
All 38 cards at a glance
Every card is also listed below so you can scan, print or review without the viewer.
Solving equations
| Question | Answer |
|---|---|
| What is a linear equation | An equation whose variable has an exponent of 1 and whose graph is a straight line. |
| What is the goal when solving an equation | To get the variable alone on one side. |
| What is the golden rule of equations | Whatever you do to one side, do to the other. |
| Solve x + 7 = 12 | x = 5. |
| Solve x − 4 = 9 | x = 13. |
| Solve 3x = 21 | x = 7. |
| Solve x/5 = 4 | x = 20. |
| Solve 2x + 3 = 11 | x = 4. |
| Solve 5x − 8 = 17 | x = 5. |
| Solve 3(x + 2) = 15 | x = 3. |
| Solve 4x + 1 = 2x + 9 | x = 4. |
| Solve 7 − x = 10 | x = −3. |
| What does no solution mean | The equation is never true, such as x + 1 = x + 2. |
| What does infinitely many solutions mean | The equation is true for every value, such as 2x = 2x. |
Lines and graphs
| Question | Answer |
|---|---|
| What is slope-intercept form | y = mx + b. |
| What is point-slope form | y − y₁ = m(x − x₁). |
| What is standard form | Ax + By = C. |
| What is the slope and y-intercept of y = 3x − 5 | Slope 3, y-intercept −5. |
| How do you find the x-intercept | Set y = 0 and solve for x. |
| How do you find the y-intercept | Set x = 0 and solve for y. |
| Write the line with slope 2 through (0, 4) | y = 2x + 4. |
| What is the slope of 2x + 3y = 6 | −2/3. |
| What does a positive slope look like | The line rises from left to right. |
| What does a negative slope look like | The line falls from left to right. |
| Write the line through (1, 3) with slope 2 | y − 3 = 2(x − 1), or y = 2x + 1. |
| What is the slope of a line parallel to y = 4x + 1 | 4. |
Systems and inequalities
| Question | Answer |
|---|---|
| What is a system of linear equations | Two or more linear equations solved together for the same variables. |
| What are three ways to solve a system | Graphing, substitution and elimination. |
| What is the solution of a system on a graph | The point where the lines intersect. |
| Solve y = 2x and x + y = 9 | (3, 6). |
| What does it mean if a system has no solution | The lines are parallel and never meet. |
| What does it mean if a system has infinitely many solutions | Both equations describe the same line. |
| Solve 2x + 5 > 11 | x > 3. |
| Solve −3x ≤ 12 | x ≥ −4 (the sign flips when dividing by a negative). |
| How do you graph x > 2 on a number line | An open circle at 2 with an arrow pointing right. |
| How do you graph x ≤ 2 on a number line | A closed circle at 2 with an arrow pointing left. |
| How do you graph y > 2x + 1 on the plane | Draw a dashed line y = 2x + 1 and shade above it. |
| When is the boundary line solid | When the inequality includes equality: ≤ or ≥. |
Frequently asked questions
How do you solve a linear equation?
Undo operations in reverse order: simplify, move variable terms to one side, move constants to the other, then divide by the coefficient.
How do you check a solution?
Substitute your answer back into the original equation. If both sides are equal, the solution is correct.
What is the difference between slope-intercept and standard form?
Slope-intercept (y = mx + b) shows slope and y-intercept directly. Standard form (Ax + By = C) is easier for finding intercepts and for elimination.
Sources
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